Subgroup and quotient

Let $G$ be a group, and $N$ a normal subgroup. Which of the following statements is/are always true?

I. If $N$ is finite and $G/N$ is finite, then $G$ is finite.
II. If $N$ is finite and cyclic and $G/N$ is finite and cyclic, then $G$ is finite and cyclic.
III. If $N$ is abelian and $G/N$ is abelian, then $G$ is abelian.

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Notation:

• A finite cyclic group is a group that is isomorphic to ${\mathbb Z}_n,$ the integers mod $n,$ for some $n.$
• An abelian group is a group whose operation is commutative: $x * y = y * x$ for all $x,y \in G.$